potential flow

potential flow [pə′ten·chəl ′flō]

(fluid mechanics)

Flow in which the velocity of flow is the gradient of a scalar function, known as the velocity potential.

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Potential flow

A fluid flow that is isentropic and that, if incompressible, can be mathematically described by Laplace's equation. For an ideal fluid, or a flow in which viscous effects are ignored, vorticity (defined as the curl of the velocity) cannot be produced, and any initial vorticity existing in the flow simply moves unchanged with the fluid. Ideal fluids, of course, do not exist since any actual fluid has some viscosity, and the effects of this viscosity will be important near a solid wall, in the region known as the boundary layer. Nevertheless, the study of potential flow is important in hydrodynamics, where the fluid is considered incompressible, and even in aerodynamics, where the fluid is considered compressible, as long as shock waves are not present. See Boundary-layer flow, Compressible flow, Isentropic flow

In the absence of viscous effects, a flow starting from rest will be irrotational for all subsequent time. For an irrotational flow, the curl of the velocity is zero (∇ × V = 0). The curl of the gradient of any scalar function is zero (∇ × ∇&phgr; = 0). It then follows mathematically that the condition of irrotationality can be satisfied identically by choosing the scalar function, &phgr;, such that the velocity is the gradient of &phgr; (V = ∇&phgr;). For this reason, this scalar function &phgr; has been traditionally referred to as the velocity potential, and the flow as a potential flow. See Potentials

By applying the continuity equation to the definition of the potential function, it becomes possible to represent the flow by the well-known Laplace equation (∇²&phgr; = 0), instead of the coupled system of the continuity and nonlinear Euler equations. The linearity of the Laplace equation, which also governs other important physical phenomena such as electricity and magnetism, makes it possible to use the principle of superposition to combine elementary solutions in solving more complex problems. See Fluid flow